The permutation group of affine-invariant extended cyclic codes


Thierry Berger
UFR des Sciences de Limoges
123 avenue A. Thomas
87060 Limoges Cedex, France
and
INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France

Pascale Charpin
INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France
Pascale.Charpin@inria.fr

IEEE Transactions on Information Theory, 42(6):2194-2209, 1996.

Abstract

Primitive cyclic codes whose extension is invariant under the affine group were characterized about thirty years ago. They form a class including codes of great interest such as BCH-codes, generalized Reed-Muller codes or Reed-Solomon codes. We present the formal expression of the permutation group of these codes. Afterwards we give several tools in order to determine effectively the group of a given code or of some infinite class of codes. In the end, we give our main application, the permutation group of primitive BCH-codes defined on any prime field.